Aug 2, 2010 - [7] T.W. Hдnsch, J. Alnis, P. Fendel, M. Fischer, C. Gohle,. M. Herrmann, R. Holzwarth, N. Kolachevsky, T. Udem, and M. Zimmermann, Phil.
PRL 105, 063001 (2010)
PHYSICAL REVIEW LETTERS
week ending 6 AUGUST 2010
Extreme Ultraviolet Frequency Comb Metrology Dominik Z. Kandula, Christoph Gohle,* Tjeerd J. Pinkert, Wim Ubachs, and Kjeld S. E. Eikema† Institute for Lasers, Life and Biophotonics Amsterdam, VU University, De Boelelaan 1081, 1081HV Amsterdam, The Netherlands (Received 28 April 2010; revised manuscript received 24 June 2010; published 2 August 2010) The remarkable precision of frequency-comb (FC) lasers is transferred to the extreme ultraviolet (XUV, wavelengths shorter than 100 nm), a frequency region previously not accessible to these devices. A frequency comb at XUV wavelengths near 51 nm is generated by amplification and coherent upconversion of a pair of pulses originating from a near-infrared femtosecond FC laser. The phase coherence of the source in the XUV is demonstrated using helium atoms as a ruler and phase detector. Signals in the form of stable Ramsey-like fringes with high contrast are observed when the FC laser is scanned over P states of helium, from which the absolute transition frequency in the XUV can be extracted. This procedure yields a 4 He ionization energy at h 5 945 204 212ð6Þ MHz, improved by nearly an order of magnitude in accuracy, thus challenging QED calculations of this two-electron system. DOI: 10.1103/PhysRevLett.105.063001
PACS numbers: 32.10.Hq, 42.62.Eh, 42.65.Ky
Mode-locked frequency-comb (FC) lasers [1,2] have revolutionized the field of precision laser spectroscopy. Optical atomic clocks using frequency combs are about to redefine the fundamental standard of frequency and time [3]. FC lasers have also vastly contributed to attosecond science by providing a way to synthesize electric fields at optical frequencies [4], made long distance absolute length measurements possible [5], and have recently been employed to produce ultracold molecules [6]. FC based precision spectroscopy on simple atomic systems has provided one of the most stringent tests of bound state quantum electrodynamics (QED) as well as upper bounds on the drift of fundamental constants [7]. Extending these methods into the extreme ultraviolet (XUV, wavelengths below 100 nm) spectral region is highly desirable since this would, for example, allow novel precision QED tests [8]. Currently the wavelength range below 120 nm is essentially inaccessible to precision frequency metrology applications due to a lack of power of single frequency lasers and media for frequency up-conversion. Spectroscopic studies on neutral helium using amplified nanosecond laser pulses [9,10] are notoriously plagued by frequency chirping during amplification and harmonic conversion which limits the accuracy. These kind of transient effects can be avoided if a continuous train of high power laser pulses (produced by a FC) can be coherently up-converted. This would transfer the FC modes, at frequencies fn ¼ fCEO þ nfrep , where fCEO is the carrier-envelope offset frequency, frep is the repetition frequency of the pulses, and n an integer mode number, to the XUV. Similar to what was shown in the visible [11,12], the up-converted pulse train could be used to directly excite a transition, with each of the up-converted modes acting like a single frequency laser. By amplification of a few pulses from the train, and producing low harmonics in crystals and gasses, sufficient coherence has been demonstrated down to 125 nm to perform spectroscopic experiments [13,14]. To reach 0031-9007=10=105(6)=063001(4)
wavelengths below 120 nm in the extreme ultraviolet or even x rays, high harmonic generation (HHG) has to be employed requiring nonlinear interaction at much higher intensities in the nonperturbative regime [15]. That HHG can be phase coherent to some degree is known [15–17], and recently XUV light has been generated based on upconversion of all pulses of a comb laser at full repetition rate [18–21]. However, no comb structure in the harmonics has been demonstrated in the XUV, nor had these sources enough power to perform a spectroscopic experiment. In this Letter we show that these limitations can be overcome, leading to the first absolute frequency measurement in the XUV. Instead of converting a continuous train of FC pulses, we amplify a pair of subsequent pulses from an IR frequency-comb laser with a double-pulse parametric amplifier (OPA) [22] to the milli-joule level. These pulses with time separation T ¼ 1=frep can be easily upconverted into the XUV with high efficiency using HHG in a dilute gaseous medium, and used to directly excite a transition in atoms or molecules [see Figs. 1(a) and 1(c)]. This form of excitation with two pulses resembles an optical (XUV) variant of Ramsey spectroscopy [13,23]. Excitation of an isolated (atomic or molecular) resonance with two (nearly) identical pulses produces a signal which is cosine-modulated according to cosð2ðftr TÞ ðftr ÞÞ, where ftr is the transition frequency and ðftr Þ is the spectral phase difference between the two pulses at the transition frequency. Ideally, this spectral phase difference is just ðfÞ ¼ qCE ¼ 2qfCEO =frep , where q is the harmonic order under consideration and CE the carrier-envelope offset phase slip between subsequent pulses of the FC. In this case the cosine-modulated spectroscopy signal has a maximum whenever one of the modes of an up-converted frequency comb would be resonant. This statement remains true even if the amplification and harmonic up-conversion significantly distorts the electric field of the individual pulses as long as these distortions are common mode for each of
063001-1
Ó 2010 The American Physical Society
PRL 105, 063001 (2010)
PHYSICAL REVIEW LETTERS
FIG. 1 (color online). (a) Spectral and temporal structure of the generated light (left to right): FC of the continous coherent pulse train from the FC laser, the cosine-modulated spectrum of a pair of amplified pulses, and odd harmonics of the amplified FC laser pulses each containing a cosine-modulated XUV comb corresponding to the XUV pulse pair. (b) Simplified 4 He level scheme, XUV comb excitation at 51.5 nm from the 1s2 ground state to the 1s5p excited state and state-selective ionization by a pulse at 1064 nm. (c) Schematic of the experimental setup. D: beam mask, L: focusing lens, f ¼ 50 cm, I: iris to separate XUV from IR. The pump laser provides both the 532 nm for pumping the OPA as well as 1064 nm for ionization of helium.
them. Distortions that are not common mode need to be monitored and corrected for, in this experiment at a level of
